Simplifying 0**x gives 0, with no assumptions on x

[pelegm]

Check this:

sage: simplify(0**x)
0

but

sage: 0**0
1

Upstream: Not yet reported upstream; Will do shortly.

Component: symbolics

Keywords: simplify

Issue created by migration from https://trac.sagemath.org/ticket/22027

[rwst]

comment:1

That is a Maxima bug.

[pelegm]

comment:2

Are we ok with sage returning 1 for 0^0? This is the case in Python, but in Maxima is it undefined.

Is maxima under active development? Should we report that issue there?

Note that sympy handles this properly:

In [6]: sympy.simplify(0**x)
Out[6]: 0**x

[DaveWitteMorris]

comment:3

Singular says 0^n = 0 (where n must be an integer):

CanonicalForm
power ( const CanonicalForm & f, int n )
{
  ASSERT( n >= 0, "illegal exponent" );

  if ( f.isZero() )
    return CanonicalForm(0L);
  ...

I would say this is clearly wrong: x^0 needs to be 1 for all x if the exponent is an integer variable.

[EmmanuelCharpentier]

comment:4

Ask Sage question 61400 makes me raise the priority of this one.

One should note that

• Sympy does not give an explicit 1 and returns the sum unevaluated
• Giac returns undef
• Mathematica raises an error claiming that 0^0 is indeterminate

Furthermore:

sage: sum(x^j/factorial(j),j,0,oo)
e^x
sage: sum(x^j/factorial(j),j,0,oo).limit(x=0)
1
sage: sum(x^j/factorial(j),j,0,oo).subs(x=0)
1

But, indeed:

sage: with assuming(j, "integer", j >= 0): 0^j
0^j
sage: with assuming(j, "integer", j >= 0): (0^j).simplify()
0

Since simplify does its work by passing its argument to Maxima,
and uses the returned value as a result, the ball is well in Maxima's camp...

[EmmanuelCharpentier]

Upstream: Not yet reported upstream; Will do shortly.

[slel]

comment:5

The "maxima-discuss" mailing list had a thread last month
about zero to the zero:

• https://sourceforge.net/p/maxima/mailman/message/37606840/

(from there click "View entire thread").